The horse-powered household

If there is one thing that I consider separates our society for all others in the past, it is a profligate use of energy. It is the incredibly cheap (historically speaking), easily accessible, stored, high-grade energy that lets our society do the things we do at the scale we do it.

The huge populations that support huge and diverse cultures of people, the instant connectivity and the insane throughput of material resources we have, all would be impossible if we used and harnessed energy in the same way any human society did less than 200 years ago.

For the next few posts I’m going to explore the world of energy, for two reasons:

  • I am utterly fascinated by energy, how its moves around us, changes form and changes us
  • Most people don’t give much thought to energy, but might find it interesting.

Dense definitions

Carrying on a little from my last post, the first thing we need to do is talk a little about how energy is measured. The international unit used for measuring energy is the Joule. Most people only come across joules outside of a science class on the nutritional information thing on the site of food packaging. Even then its supplied alongside calories which is the thing many people pay attention to instead.

A joule is the amount of energy transferred to an object by moving an object one metre against a force of one Newton. You don’t need to know what a Newton is, but on Earth the force of gravity means that an object weighing 100 grams is exerting a force due to gravity of about one Newton. Want to produce a Joule? Lift a small apple up a metre. That’s the work in one joule.

The William Tell Moment: An additional 1 Newton to an already weighty head proved too much.

We will look at how the joule relates to other units in a minute, but firstly its necessary to create distinction between two related but different concepts: energy and power.

The difference matters when we try to think about energy, but even national newspapers will get this mixed up on a weekly basis. It is poorly understood but I am going to have a try at explaining.

Watt horse?

First lets talk about power and lets start with a unit that should make sense to most people. The horsepower.

The person history gives credit to for developing the horsepower is James Watt. Contrary to popular opinion he didn’t invent the steam engine. James Watt did make the steam engine far more efficient, had a lucrative business model and had the patent office grant him a monopoly for a long time, but he didn’t invent the steam engine. Popular contenders for that honour are Hero of Alexander and Thomas Newcomen.

James Watt did, however, come up with a way of comparing the performance of a steam engine with that of a draught horse, mainly for marketing purposes. The story behind how  an exact figure was arrived at is a little unclear, but in one version it was based on how quickly a draught horse could work at a mill. The units initially used were in foot-pounds per minute over a working shift for an animal (about 4 hours). That is, a horse was able to turn a mill wheel of 12 feet in radius, 144 times per hour, whilst the wheel resisted (by grinding grain) with a force of 180 pounds (800 Newtons). These figures varied, of course, and what we now have is a little different. Broadly speaking there are two definitions of horsepower in use today:

  • Mechanical or Imperial horsepower: 33,000 foot-pounds per minute (rounded up from the above example’s 32,572 ft.lbf/min)
  • Metric horsepower: the power needed to lift the weight of a person (75 kg) one meter in one second.

The horsepower is abbreviated to hp in English, CV in other European countries (Caballo de Vapor – Steam Horse in Spanish and equivalent literal translations in Italian, Portuguese and French) and PS in German for Pferdestärke (Horse Strength), because Germany.

A simple diagram of what a horsepower might look at. The box on the right will be lifted a metre in one second by the power of one horse. Link.

The horsepower is still widely used when discussing the mechanical output of engines. although it generally isn’t used when talking about thermal power, electrical power, electromagnetic or radio frequency power and others. For measuring these we can use the Watt, the unit of power measurement named after James Watt to describe something that he already came up with a unit for.

A Watt can be converted by multiplication to a horsepower and vice versa. One imperial horsepower is 746 Watts, a metric horsepower being 735 Watts. To make the units easy in the next part I am going to call one horsepower 750 Watts, less than 1% more than an imperial horsepower. Someone gave our horse a sugar cube.

In summary, horsepower and the Watt are both a measure of power.

Joules Burn

Now lets go back to energy and the Joule. Recall that one Joule is the energy taken to raise approximately 100 grams one metre up against gravity. Multiplying by 10 means lifting up 1 kilogram takes 10 Joules. Multiplying by 75 means lifting 75 kilograms one meter high expends 750 Joules of energy.

The key thing to note about these 750 Joules is that they don’t care how long anything takes. Want to use a jack to make is easy to lift 75kg and spend 5 minutes jacking? The result is still 750 joules (plus friction in the jack) when that 75 kilograms it listed up 1 metre.

A horsepower is all about time. In the diagram above, a horsepower lifts 75 kg up one metre in one second.

Power is the rate of energy output.

Apply one horsepower for 1 second? 750 Joules of output. 10 seconds? 7500 Joules.

Energy is how much work is done by the power when it is used for a certain time.

Your electricity company doesn’t bill your for Watts. It bills you for energy, expressed in Watt-hours.

A Watt-hour is like measuring labour in man-hours. It may as well be called a horsepower-hour, that way people might understand what they are paying for.

The horse-powered house

The average household in Australia consumes 18 kilowatt-hours, or 18,000 watt-hours per day. Most of that energy is likely to be coming from a turbine of some kind: steam, gas, hydroelectric or wind. Imagine if that energy supplied by draught horses turning a generator like they did a pump or mill wheel? How many horses would that take?

The 18,000 Watt-hours used in a 24-hour day by the average Australian household means that 750 Watt-hours used every hour. This works out to an average power of 750 Watts – exactly the same as the output of a draught horse. Only one horse per house? That’s not so hard to imagine, at least for a fully-detached house.

The reality is that horses need to rest just like all organisms and a four-hour shift was considered the norm in the days of animal power, at least it is what James Watt used in his marketing. Taking that at face value means that to supply our 24 hour requirement for on-demand power we would need 6 draught horses working in four-hour shifts each.

According to the NSW Department of Primary Industries, the amount of land required to support a draft horse is 14 Dry Sheep Equivalent. I know, I know. Simplistically, it’s just a measure of land productivity and carrying capacity.

1 Dry Sheep Equivalent is the amount of land required to support one 2-year-old, 45 kg wether or non-lactating, non-pregnant ewe. In the area where I live now – some of the most productive country in Australia – the average stocking rate is 15.1 DSE/hectare. Using this measure we need about one hectare to supply one draught horse. In order to supply the average Australian house with it’s 6 draught horses for 24-hour electricity we will need 6 hectares.

6 hectares is 60,000 square metres. By way of a rough comparison Solar Photovoltaic panels would would need only about 25 square metres to generate those 18 kilowatt-hours, or under 2000 times less area. In both situations, some form of energy storage is needed to supply energy when higher-than average requirements were made or during a gap in energy production.

The 6 hectares of land that would be needed to keep my house humming on contemporary sunlight – as opposed to the ancient kind in fossil fuels – is quite a bit more than the 1/10 hectare my house sits on. The work done by fossil fuels is equivalent to 10 billion human slaves working 24-hours a day in output, giving us in the western world a standard of living inaccessible to even royalty a couple of centuries ago.

When flipping the switch on the kettle summons the instant power of 3 draught horses out of a skinny little cord from the wall, it’s not hard to understand why the convenience of instant energy is so addictive.

With that thought I’m off for another fortnight. Next time I’m going to explore what a litre of petrol or short ton of coal actually represent and why when compared to animal power their use became a huge windfall.


I’m curious to know how you found this post. Too dry? Too numbers-heavy? Too long? Unreadable?

Leave your thoughts below, I’m keen to not just have a conversation with myself and if this post brings on any questions, let me know that too.


Farts per million

“If you think you are too small to make a difference, try sleeping with a mosquito.”

Dalai Lama XIV

I always liked this quote, but felt it didn’t have enough data behind it. It’s fine to say that small things really can make a difference, but how small are these things really?

To find out we are going to need some way of measuring the things in question. We have ways of measuring weight, in grams, kilograms and tonnes (which is also called a megagram, but no-one calls it that). To be totally correct we would be measuring weight but calling it mass and using the units for mass, not weight. But we’re, like, not going there. At least today. Forget I said anything about mass.

Let us instead consider how much space something takes up: volume. For this we can use litres, cubic metres, acre-feet, and a variety of other things. We won’t be using acre-feet today.

To start off on this explanation of little things that impcat bigger things I want to explore the event that at least some people have experienced or been a direct participant in, willing or otherwise, that of the gas-passing individual in a more or less airtight space. Put simply we’re talking about a fart in an elevator.

To start off we first need to know how big our elevator is. I wasn’t having a whole lot of success finding out the most popular elevator in the world, so I decided to measure the one at work. As a side note, measuring the inside of an elevator with a tape measure isn’t considered normal behaviour in the office environment – especially when you are the new guy – but at the time it felt like a reasonable thing to do.

The elevator in my building is a lovely little Finnish number, of the Kone marque. This elevator measures 2.4 metres high, a trim 1.4 metres front to back and a hefty, baby-got-back 2 metres wide. I don’t know much about elevators but I know what I like. This elevator’s total volume  is 6.7 cubic metres.

It seems if there is ever a question you may have, someone has asked it before and possibly done a lot of work in the process. So it goes with flatulence. According to a study conducted at Royal Hallamshire Hospital in Sheffield where 10 volunteers ate their normal diet plus 200g of baked beans a day, the volume of gas produced by a healthy human through flatulence was between 476ml to 1491ml per day (at atmospheric pressure). The most likely amount of gas produced was 705ml of gas and no difference was recorded between male and female volunteers. Also, most participants didn’t fart any methane (only three of the ten did). There you go.

Whilst knowing how much gas a day someone may make may be nice for posterity (ugh), what we really want to know is how big a flatulence event is.  Furthermore to find out the concentration of noxious gases in our hypothetical elevator we need to know what is in that gas.

The British study doesn’t disappoint: the volume of a single fart – politely called an ’emission’ – ranges from an asthmatic 33mL on the low end to a full rip-snorting 125mL at the high end, with a median (that’s the middle, not average) volume of 90mL. 90mL is about a third of a cup.

Another study that looked specifically at the composition of flatus (yes, that’s the name they use) noted that most of the gases in a fart have no odour. In fact 99% of the gas composition is odour-free. That means that the aforementioned 125mL widow-maker has less than 13mL of odour-causing gas in it. The smelly gases? Well the prime culprit is hydrogen sulphide (rotten egg gas), followed by big-hitters methanethiol and dimethyl sulphide with others in smaller amounts.

Back to the elevator. With its volume of 6.7 m³, 13mL makes up just under 1.9 parts per million of the total gas in that elevator. In reality people will take up a bit of the space as well,  say 0.1m³ per person. By probability the more people there are, the greater chance of an emission occurring and also the greater the fraction of the free air in the elevator the fart occupies. I smell trouble brewing.

Anyway, of all the gases in that box pretty much the only ones that matter are the ones in 13mL of volatile substances that your body produces, and that’s a worst case scenario. Our noses are actually far more sensitive to odours than that, even a faint whiff of fart is enough to elicit funny face contortions from the unlucky passerby.

There has been a good deal more research into the sensitivity of human smell than I am prepared to go into. Apparently, humans have quite a good sense of smell even when compared to other animals, including dogs. Knowing what dogs like to smell I personally wouldn’t exactly be putting my hand up to have a go at comparison for science. Studies other than what I have just described look across a range of different things we can smell, some which we can detect even when their concentration is less than one parts in a billion, like the odourant added to BBQ gas. One part per billion is like a tablespoon of water compared to 5 Olympic swimming pools.

Now just for fun, lets look a little at the quote we started out with regarding mosquitoes. Many common mosquitoes in Australia range from 4 to 6mm in length. If we split the difference and make some generalisations we might say that a mosquito flying about and flapping its wings would fill up a sphere with a 5mm diameter. This means our mosquito fills up a volume of 65.5mm³ (cubic millimeters). For context – assuming I can find context for this – there are 1000 cubic millimetres in a millilitre, which is one thousandth of a litre. It’s very small and confusing.

I couldn’t find statistics for bedroom size in Australia, but a bit of a look on renovation forums suggests that somewhere between 3 x 4 metres and 4 x 4 metres is pretty standard for a bedroom, so again we will split the difference and say that 3.5 x 3.5 metres is a pretty standard floor area for a bedroom. The Building Code of Australia has a minimum ceiling height of 2.4 metres, so lets take that too. That gives a room volume of 29.4 cubic metres.

If one were to apply (some may say misuse) the concept above looking at the volume taken up in a room, but instead of a fart consider a mosquito, we find that in terms of the volume occupied, a mosquito makes up 2.23 parts per billion of the room. Therefore, in summary and using a completely flawed comparison, mosquitoes are roughly 1000 times more annoying than the smelly parts of a fart on a volume/volume basis.

Is there really a hole in the ozone layer?

Quite a few years ago whilst having a beer with my father in an Irish-themed Canberra pub and in discussion with a couple of former panel-beaters a statement was made that questioned the existence of a hole in the ozone layer. At the time I dismissed it as being a sort of weird fringe idea like faked moon landings or that full fat tasting skim milk exists.

It turns out that it’s not that fringe.

Now of course air in the Donald’s hypothetical apartment is exchanged with the outside atmosphere through heating and air conditioning systems, leaks and gaps in the building envelope and of course actual openings like doors and windows. Human beings and in fact all organisms that breathe oxygen (and even those that don’t) need to exchange gases with the atmosphere and cannot survive for long periods in sealed boxes. So the hypothetical hairspray will find its way out of the hypothetical apartment, even the good hairspray that lasts longer than 12 minutes.

I’m not going to explore in this post whether or not it is actually a good idea to use the atmosphere as an aerial sewer for all of the excess products and waste of our lifestyles, at least not today. What I do want to talk about here is how this whole ozone hole thing works when we can’t see it, what it has to do with hairspray and what it has to do with cancer. To address this, I’d first like to talk a bit about light.

You might be thinking “I know about light” and I’m sure you do. But bear with me, because light has some crazy properties that we need to talk about to get to the bottom of this story.

The light that we – two-legged walking sacks of water like you and me – use to see things in our daily lives isn’t the only thing that is shining in our faces, its just the stuff our eyes can detect. Our eyes are suited to a particular type of light that we call – sensibly enough – visible light. Our ears are kind of the same in that they can only hear certain frequencies of sound. This works fine for a musical instrument but isn’t so great for hearing the high pitch sound that a dog whistle makes (ultrasound), nor does it work for the low frequency vibrations created by a highway or a wind turbine (infrasound – oh look, more blog topic material!).

White light is made up of all of the colours we can perceive. A cloudy moonless night sky is the opposite – total darkness.

The types of light that our eyes can detect form a part of a spectrum of light which is arranged by the wavelength of light. We don’t need to go into this though, all we need to know is that we see blue, green and red light and that each of those colours is but a thin slice of the electromagnetic spectrum as a whole.


Electromagnetic spectrum
Your TV can see some of these waves, the cells in your body may see others but the only ones we consciously observe as vision are the coloured ones that our eyes can see..In the coloured bar at the right you will notice that above the blue light is a thin strip of violet. Above violet is ultraviolet.

In the image, below the red end of the spectrum that we can see is an area that we call infra-red. Infra? Well that means below. Infra-red light is the energy given off by an object that relates to its temperature. We can detect infra-red light only by feeling it with our skin. We are very insensitive to it which is why we need to get very close to that kettle before we can tell if it has boiled recently or not. Our skin is sensitive to heat but not enough to detect a detailed image or at a distance. It is only as good as being able to tell shades of light from a very close distance. We are effectively blind to the infra-red world. Some snakes have a kind of vision (although it isn’t vision like we know it) that is able to detect heat to such a degree that it can use it to hunt. Of course this has been investigated by experiment, because no one has seen what a snake sees. Or have they?

Ever wondered how a TV receives the signal from the remote? A little LED in the remote control emits only infrared light and the TV only picks up infrared light. If you could see the infrared part of the electromagnetic spectrum you would see it flashing, but you don’t. Likewise you don’t see even longer wavelength radio waves, but your radio can pick them up.

Wasn’t this about the ozone hole?

Okay, so there are different kinds of light and with some fancy equipment we can detect when it is around when our eyes alone won’t do the job. Now on to ozone.

Ozone is an unstable molecule made of three oxygen atoms. The oxygen that we breathe has only two oxygen molecules (O2). One could say that ozone is therefore 50% better, but one would be oversimplifying greatly.

This is molecular oxygen, the type we breathe. It has two oxygen atoms that just love hanging out together.
This is ozone, with an extra oxygen atom hanging in there. This can’t last.

When it comes to how oxygen atoms hang out, two is a party and three is a crowd. The extra oxygen atom makes ozone very reactive. This is because whilst oxygen atoms are tight and happy just hanging together when there are only two, the extra oxygen atom can only ever hang on quite weakly and will always be the outsiders.

With enough oxygen and a spark you can even burn metal. Whilst not burning exactly, with a spare oxygen atom hanging on, ozone can react with things very quickly and without a spark. It is sometimes created artificially and used in a practical way to treat water as it reacts with germs and micro-organisms and – again simplistically – burns them into carbon dioxide and water. Ozone also has a smell, something oxygen doesn’t. If you’ve ever been around power tools or blending something up really well in the kitchen you have probably smelt ozone. It’s that electric motor smell. The ozone forms from oxygen in the air and is created in the little sparks that occur around some types of electric motor.

But, but, hairspray!

Chlorofluorocarbons – from here on CFCs – were regarded as wonder chemicals when they were first developed back in 1928. They are non-toxic, non-flammable and really good refrigerants. Previously ammonia had been used as a refrigerant in household appliances but had the nasty side-effect of killing the people in the house if it leaked. Because of their properties CFCs were used widely, including as hairspray propellant. In addition to working really well (apparently) hairspray with CFC propellant wouldn’t become a flamethrower in the hands of a teenager or arachnophobic householder.


CFCs are also really light which means they float really well. High in our atmosphere, a bit above where airliners fly (10km high) and for another 30 km higher there is a much higher concentration of ozone than normally occurs at ground level. This is called stratospheric ozone. Most of the ozone that is measured in the atmosphere on Earth is in this zone. This is known from using sensors to measure the presence and concentration of different gases in the atmosphere. There are a number of different methods for detecting ozone concentrations, including sensors similar to those that keep an engine with modern fuel injection running properly by detecting oxygen in the exhaust gas.

So we know we can detect ozone, we know that there is more ozone high up and we know that CFCs can float to where the ozone is.

Come back from the light

Lets flip back to the electromagnetic spectrum for a moment. You will be aware that certain materials are better at letting light through than others. Think coloured cellophane, which reflects some parts of visible light and lets others through. The image sensors in digital cameras – like the ones in a smartphone – are actually sensitive to the infra-red light we were discussing earlier. To prevent them from taking a photograph that displays things that you cannot see, filters are placed over the lens so that the infra-red light is blocked but visible light is allowed to pass.

In this image a video camera without an infrared light filter displays an image on the screen (there may be a source of infrared light in the room). To take the photograph of this scene, the camera that produced the above image would have to have been filtering infrared light.

Liquids and gases can also behave this way. Chlorine gas has a greenish appearance (chloros meaning green in ancient Greek and the reason for its name), because it reflects green light. Carbon dioxide absorbs infrared light whilst letting other pass, which is why it is a greenhouse gas.

It so happens that ozone in the atmosphere acts likes a filter for a particular slice of ultraviolet light-containing sunlight called UV-C. Parts of the UV spectrum called UV-A and some UV-B reach the surface of Earth and is what ruins plastic that has been left out in the sun too long. If UV light were visible light, UV-A would be red, UV-B would be green and UV-C would be in the blue-purple end. The higher in frequency (closer to the blue end) the light is, the higher in energy it is.

Whilst UV-A  can ruin your plastic bucket and can cause sunburn, UV-B and UV-C even more is a problem for just about everything that lives.

UV-C is very high energy. UV-C light is used in some water treatment systems to kill microorganisms. It is powerful stuff. This means it can destroy living cells. Skin cells of all kinds, plant and algae cells. It is this cell damage that can lead to skin cancer.

With an intact layer of ozone UV-C and parts of UV-B light is completely absorbed. The ozone (three oxygens) in the atmosphere is in fact created by this high energy UV light interacting with our normal, good-to-breathe oxygen (two atoms). This is a nice little trick for all of us down here on the surface as the protective shield of ozone, is continuously replenished by the very thing it is protecting us from.

The problem is when U.V. Light meets CFC McC Face.

UV light is powerful enough to cause cell damage in plants and animals, and powerful enough to crack 3 diatomic oxygen and make 2 ozone from its leftovers. It’s also powerful enough to knock the first C in CFC (Chlorofluorocarbon) right out of there, creating free chlorine gas.

Chlorine gas is like the twin sister to ozone and UV light. It is also highly reactive, it is also used to kill things, including likely in the water you drink from the tap. When two reactive chemicals inhabit the same space they tend to react with one another, and that’s what happens when chlorine gas and ozone get together. When this happens ozone is consumed more quickly than sunlight can replenish it and the layer of gas that protects Earth’s biosphere from the sun that also provides all their energy starts to disappear.

You might be thinking that surely there must be an upside to ozone depletion, right? Like if there is more incoming energy passing through the atmosphere, “does that mean my solar panels will produce more power when there is an ozone hole above me?”. Perhaps that is just me. The answer is no. Even though ultraviolet light is energetic, the part of the electromagnetic spectrum that the most common solar panels get derive the power from is roughly the same as the human eye. Some types are a bit more sensitive to infra-red red, others a little more to ultraviolet, but the contribution to their total power is many times less than visible light. There is no merit in an evil genius plan for growing the ozone hole and getting more power from solar power, at least using today’s commonly available solar panels. Anything else would be uneconomic and therefore whilst conceivably evil, would fail at the genius part.

I hope this has covered off what I led you to believe I was to talk about, that being how there could be a hole in the ozone layer and what it has to do with CFCs and cancer. This article outgrew its initial concept by a long way. For someone as ill-informed about hair styling as myself I have wondered a few times if it was worth continuing with. Nevertheless I will be back next week with a far shorter article seeking to answer technical questions that many never thought to ask. See you next time!

Happy Birthday to me, I’m 0x20 years old!

This week I celebrated my birthday and I thought it would be fun to talk about binary and hexadecimal numbers. Yes that’s right, fun.

One of the thoughts first had when I thought I would write this blog was that less outwardly nerdy people might read it and work out what all those nerd were laughing at with their nerd jokes. Then again, most people aren’t interested in those kind of jokes.

A lot of people know that computers use 1s and 0s to do their thing but less people know how or why. I’m going to talk about that a little bit. The reason that there can be a 1 or a 0 is that computers are made up of heaps of switches. You are reading this on a device that has many many millions of them. These work in the same way as a light switch. Not a fancy dimmer switch though, these switches can only be on or off.

Also, in simplistic terms computers work by taking instructions from a program, running those instructions on data and then presenting the results. In order for instructions and data to represent meaningful things, you need to be able to use those switches in a way to represent data and instructions. This is the idea behind the binary number system.

We humans have 10 fingers, including thumbs. It’s no coincidence then that a great many cultures (not all) use what is called a base-10 counting system or decimal numbers. Once we count to ten, we need to start using our toes or remembering what many tens we are up to (was I up to 66 or 76?).

Computers can do the same, but with only one switch you can only represent 1 or 0. As there are only two numbers something can be we call this base-2 counting, or binary numbers. To represent useful numbers you need to use more than one switch.

We call these switches bits.

Let’s look at a simple example with four bits. Bit one will represent the number 1 or 0, bit two will represent 2 or 0, bit three 4 or 0 and bit four is 8 or 0. Depending on which bit or bits are turned on we can represent with combinations of these any number between 0 and 15.

Below are some examples. On the left are three different numbers represented using 4-bit binary. On the right is how those numbers are calculated. Don’t worry too much about the calculation:

0000 = 0              (0 x 8) + (0 x 4) + (0 x 2) + (0 x 1) = 0
0101 = 5              (0 x 8) + (1 x 4) + (0 x 2) + (1 x 1) = 5
1111 = 15             (1 x 8) + (1 x 4) + (1 x 2) + (1 x 1) = 0

It often occurs to me that someone really smart had to have been responsible for thinking that this is even possible, but now we treat this stuff as given and use it all the time.

Often when writing numbers out like this in binary, the number is preceded by a 0 and then a ‘b’ to show that the number is in binary. So 15 in binary is 1111 and would be written 0b1111 to avoid confusion with one-thousand, one-hundred and eleven. Larger numbers can be represented using more bits. Depending on the computer processing the numbers, it may be able to calculate the number in one go, or it may need to split up the calculation into manageable parts (like performing long division with and pen and paper).

In the 1970s the first microprocessors to be implemented in pocket calculators and the like were 4-bit processors. This meant that they could only work on numbers 4 bits in value at one time. Later, more complex processors were developed that could work on 8 bits at one time and this let them represent numbers between 0 and 255. These types of processors were used in the first personal computers like the Apple II and the Commodore 64 (the 64 stood for the amount of memory, not the number of bits). 16 and 32 bit processors became used in IBM compatible PCs and video game consoles and only recently personal computers have started to use 64 bit processors.

64 bits are a whole lot of bits. It means that very large numbers can be represented. As an example, the maximum number in a 64 bit system would be represented by 64 ‘on’ switches. In binary we would write this as:


and the decimal number that is equal to is:


I don’t even know how to say that number but I know it ends in “illion”. Obviously representing large numbers in binary quickly becomes impractical. Even with 8 bits numbers can be time consuming to write in a form computers can operate on. Representing numbers with 8 bits in binary is still a pain:

0b1111 1111 = 2550b0100 0100 = 68

Luckily, some more clever people came up with a method to do this in a simpler way. With a small change there is a system that is easier for people to read whilst being simple for computers too. This system is called hexadecimal and it is base-16 (hexas meaning six and decem meaning ten in Latin and ancient Greek respectively). Because of the way binary systems work base-16 is actually very simple for a computer to decode and it is much better for people than binary. Hexadecimal systems use 0x (a zero and then a x) before their number so as not to confuse us again with good old decimal numbers.

Counting in hexadecimal uses the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F. The first ten numbers should make sense. After that:

0xA = 10
0xB = 11
0xC = 12
0xD = 13
0xE = 14
0xF = 15

A computer can work this out because one digit from 0 to F of hexadecimal is equal to four bits of binary, which we said can count from 0 to 15 also. If you put two hexadecimal numbers together you can represent 8 bit numbers.

0x00 = 0
0x09 = 9
0x0A = 10
0x10 = 16

I should note that none of this comes naturally, it all comes from practice. I hope that by reading this you simply understand that much of this stuff isn’t super complicated, its just simple patterns that take learning.

In the title of this post I noted that this week is my birthday when I have turned 0x20 years old. If 0x10 is sixteen, then 0x20 is twice as many.

I turned 32 years old.